Finite Group Databasebeta

← #34059955

Subgroups — #34059955

Order 19072.

236 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 64 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750645C212yesmaximal
2#23750471C214yesmaximal
3C2×#18011876C211yesmaximal, characteristic
4#18011978—22no—
5C22⋊#11924753C2214yes—
6#18011966—22no—
7C22×Dic298C411yescharacteristic
8#18011876—22no—
9#18011876—22no—
10C2×#14558715C2212yes—
11C2×C4×Dic149C412yes—
12C2×C4×Dic149C2211yescharacteristic
13C2×C4⋊C4×C149C411yescharacteristic
14C2×#11924753—24no—
15C2×Dic298—24no—
16C2×Dic298—22no—
17C22×Dic149C2×C411yescharacteristic
18C22×Dic149C2×C412yes—
19C22×Dic149C2311yescharacteristic
20#14558715—24no—
21C4×Dic149—22no—
22C4×Dic149—22no—
23C4×Dic149D412yes—
24C4×Dic149D412yes—
25C22×C4×C149C2×C411yescharacteristic
26C22×C4×C149C2×C412yes—
27C4⋊C4×C149—22no—
28#11924753—44no—
29Dic298—28no—
30C2×Dic149—22no—
31C2×Dic149—22no—
32C2×Dic149—22no—
33C2×Dic149—41no—
34C2×Dic149C22⋊C411yescharacteristic
35C2×Dic149C22⋊C411yescharacteristic
36C2×Dic149M1614yes—
37C2×Dic149C2×D412yes—
38C23×C149C22×C411yescharacteristic
39C2×C4×C149—22no—
40C2×C4×C149—22no—
41C2×C4×C149—42no—
42C2×C4×C149C22⋊C412yes—
43C22×C149—21no—
44C22×C149—21no—
45C22×C149C2×C22⋊C411yescharacteristic
46C22×C149C2×M1612yes—
47C4×C149—22no—
48C4×C149—42no—
49Dic149—24no—
50Dic149—22no—
51Dic149—21no—
52Dic149#10112yes—
53C2×C149—22no—
54C2×C149#40711yescharacteristic
55C2×C149#41011yescharacteristic
56C2×C149C2×#10111yescharacteristic
57C149#146711yescharacteristic, complemented, Sylow
58#1467—1491nomaximal, Sylow
59C2×C4×Q8—1491no—
60#432—1492no—
61#324—1494no—
62C22×Q8—1491no—
63C4×Q8—2982no—
64C4×Q8—2982no—
65C2×C4⋊C4—1492no—
66C2×C4⋊C4#1059701011yescharacteristic
67C2×C42—1492no—
68C2×C42—1491no—
69C4⋊C8—2982no—
70C22⋊C8—1494no—
71#97—2982no—
72C2×Q8—2984no—
73C2×Q8—2982no—
74C22×C4—1491no—
75C22×C4—1492no—
76C22×C4—1491no—
77C22×C4C2×#1059701012yes—
78C22×C4C2×#1059701011yescharacteristic
79C2×C8—2984no—
80C4⋊C4—22no—
81C4⋊C4—2984no—
82C42—2982no—
83C42—2982no—
84C42—1492no—
85C42—1492no—
86C23C22×#1059701011yescharacteristic
87Q8—2988no—
88C2×C4—22no—
89C2×C4—22no—
90C2×C4—42no—
91C2×C4—2982no—
92C2×C4—2982no—
93C2×C4—2982no—
94C2×C4—5961no—
95C2×C4—1491no—
96C2×C4—1492no—
97C2×C4—1494no—
98C2×C4—1491no—
99C2×C4C22⋊#1059701012yes—
100C8—5964no—
101C22—21no—
102C22—21no—
103C22C2×C22⋊#1059701011yescharacteristic
104C22D149⋊M1612yes—
105C4—22no—
106C4—42no—
107C4—2984no—
108C4—2982no—
109C4—2981no—
110C4—1492no—
111C2—22no—
112C2#2375059711yescharacteristic
113C2#2375060511yescharacteristic
114C2D149⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutator, prime radicalC23×C149C22×C4
FrattiniC23C22×#10597010
FittingC2×C4⋊C4×C149C4
socleC22×C149C2×C22⋊C4
cosocleC22×Dic149C23
hypercenterC2×C4⋊C4#10597010
hypocenterC149#1467
LCSG ▷ C23×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
57. C149#1467semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237506452
#237504712
C2×#180118762
#1467149